KI HAVE considerable covalent charecter due to polarisation , polarisation means distortion of electron cloud of anion by cation , it increase with increase in the atomic size .
as cl ion is smaller the polarisation is less , and not much covalent charecter ,
covalent substance dissolve in organic solvents , therefore KI having some covalent charecter dissolves but kcl does not .
HOPE IT CLEARS
ALL THE BEST ..